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  • AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.

AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD?

Give reason for your answer.

Answers (1)

True

Solution.        

Let triangle be AB with median AD

AD is the line bisecting BC

\Rightarrow BD = CD

\because sum of two sides of a triangle is greater that third side.

In \triangleABD

AB + BD > AD           …(i)

In \triangleADC

AC + DC > AD           …(ii)

Adding (i) and (ii)

AB + BD + DC + AC > 2AD

(\because BD + DC = BC)

AB + BC + AC > 2AD

Hence proved

Posted by

infoexpert24

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